This four-part E-Example from Principles and Standards for School Mathematics of the NCTM standards highlights how mathematical games can foster mathematical communication as students explain and justify their moves to one another in a fraction game. In addition, a video is included that demonstrates students engaged in thinking about and applying their mathematical concepts and skills. The game "Playing Fraction Tracks" is cataloged separately.

This familiar game can be played by one or two players taking turns. Players choose to match equivalent representations of numbers, shapes, fractions, or multiplication facts. The game can be played in clear pane mode, or for added challenge, with the windows closed.

This interactive Flash game at the Visual Fractions website gives students open-ended practice with combining fractions as parts of a whole. Students are given varying sets of wedges representing a mix of unit fractions. They construct whole circles (cookies) by combining the pieces, or by naming the fractional balance needed to complete each cookie. Instructions (below the applet), feedback, a timer, and a rate of cookies per minute are provided.

With this flexible Flash applet students can explore a wide range of concepts, including addition and subtraction, factors and multiples, fractions, ratios, and combinations. Users place, move and rotate virtual Cuisenaire Rods on a grid which can be enlarged, reduced, moved or printed. It contains a link to page of challenges which can take advantage of this tool.

This three lesson unit (15-page pdf) presents activities that guide students to understand the probability terms "certain" and "impossible". In each of the first two lessons students work as a class to conduct an experiment, complete sentences about the contents of a mystery bag, write probability statements, and express probability as common fractions. In the final lesson the class hears a story that contains both certain and impossible events. Students discuss which events are certain and impossible, and then construct a class book illustrating these concepts.

This problem provides students practice in fractions (tenths) and challenges students' addition and subtraction skills. Students are given a cake with the numbers zero to nine on it. They are asked to cut the cake into three pieces with three cuts so that the numbers on each piece add to the same total. The Teachers' Notes page offers rationale, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of the problem.

This problem requires students to have a good understanding of fractions and challenges children to visualize 3D shapes. Students are asked how to divide a doughnut into eight equal pieces using only three cuts. The Teachers' Notes page includes rationale, suggestions for implementation, discussion questions, and ideas for extension with a link to a worksheet and support.

This article describes the progression from halves, to thirds and fourths, as well as fair sharing as a means of teaching more abstract fractions to young students. Throughout the article activities are suggested to support the learning, as well as a link to a six-minute video which shows two children working on a difficult sharing situation practically with a teacher who questions appropriately to get the thinking going. Two of the activities mentioned in the article, "Happy Halving" and "Bowl of Fruit" are cataloged separately.

This interactive Java applet helps users explore equivalent fractions through partitioning circles and squares. The applet provides a random fraction and the user creates one or two equivalent representations of that fraction by partitioning and coloring a square (or circle). The applet also plots the fraction on a number line and points from the shape to the number line displaying its equivalent value after the fraction is built. Options include choice of circles or squares, one or two equivalent fractions, and a scoring feature allows users to keep track of the number correct.

This interactive Java applet helps users explore equivalent fractions through partitioning circles and squares. The applet provides a random fraction and the user creates one or two equivalent representations of that fraction by partitioning and coloring a square (or circle). The applet also plots the fraction on a number line and points from the shape to the number line displaying its equivalent value while the fraction is being built. Options include choice of circles or squares, one or two equivalent fractions, and a scoring feature allows users to keep track of the number correct.